Yeah, you will hear a lot of Portuguese speakers saying it like this. If you hear it enough you will get used to it. The key is understanding that a verb in the 2nd (tu) or 3rd (ele/ela/você) person never ends with "o" (like AdrianoMai1 said).
I can distinguish the two sounds. Afterall, "ele explico" is impossible (ELE explicA ou EU explicO).
Can "modelo" refer to a non-physical model like a business model? What about people?
Sure! Business model = modelo de negócio.
And yes, it can refer to that fashion people. In this case you have to pay attention to the gender because it can be both (we call "substantivo de dois gêneros"). Example: "Gisele Bündchen é uma modelo famosa".
I put " he explains to his model" anyway, "he explains his model" doesn't make sense in English!!
How do we know that he is explaining 'his' model and not 'your' model. Doesn't seu mean both?
Yes, it means both. Only context will tell. Duo should accept both translations. If it doesn't, report it.
Sometimes we can use some workarounds, like saying "ele explica o modelo dele". It is ok in spoken language, but it is not advisable to write, unless it is an informal text. In the other hand, never say "ele explica o modelo de você". Sounds like a toddler speaking.
That would be "ele explica do seu jeito" (more common) or "ele explica a seu modo" (more formal). Notice that, just like in English, you need a preposition before an indirect object. In the given examples, the prepositions "de" (contracted with article "o") and "a".